defmodule BinarySearch do
  @doc """
    Searches for a key in the tuple using the binary search algorithm.
    It returns :not_found if the key is not in the tuple.
    Otherwise returns {:ok, index}.

    ## Examples

      iex> BinarySearch.search({}, 2)
      :not_found

      iex> BinarySearch.search({1, 3, 5}, 2)
      :not_found

      iex> BinarySearch.search({1, 3, 5}, 5)
      {:ok, 2}

  """

  @spec search(tuple, integer) :: {:ok, integer} | :not_found
  def search({}, _value), do: :not_found
  def search(numbers, value), do: do_search(numbers, value, 0, tuple_size(numbers) - 1)

  defp do_search(_numbers, _value, from, to) when from > to, do: :not_found
  defp do_search(numbers, value, from, to) do
    middle = div(from + to, 2)
    element = elem(numbers, middle)
    cond do
      value == element -> {:ok, middle}
      value < element -> do_search(numbers, value, from, middle - 1)
      value > element -> do_search(numbers, value, middle + 1, to)
    end
  end
end